BACKGROUND OF THE INVENTION
This invention relates to an apparatus for sensing the relative motion of a second object some distance from the reference sensor without the need of transmitted excitation such as electromagnetic or sonic radiation. In particular, this invention may be used for the rapid measurement of the ground speed of an aircraft while flying at various altitudes.
It is often advantageous for an aircraft to be able to determine rapidly and accurately its ground velocity, as opposed to its velocity with respect to the air. For example, the knowledge of accurate ground speed during the approach and landing phases of the aircraft's operation can provide much useful information for aircraft safety. Knowledge of true ground velocity can improve the proper initialization and operation of the wheel brake anti-skid control system by providing necessary data to the hydroplaning and touchdown spin-up logic of the control system. Also, a continuous comparison between the indicated air speed and true ground speed gives an accurate measurement of the wind component along the axis of the aircraft. This information is essential for determining potential wind shear problems that the aircraft may encounter during approach and landing, and allows the proper correction of the characteristics procedure to be made in order to avoid those potentially disastrous problems.
Other concepts for determining the ground velocity of an aircraft present certain disadvantages. They often rely on a relationship (e.g., cross-correlation) between signals transmitted and received by the aircraft. Thus, they require the aircraft to carry a transmitter, a transmitting antenna, and an energy source for supplying the transmission power. These components add undesirable bulk, weight, and hence expense to the aircraft navigation system. Because these systems depend upon a transmitted signal to bounce off an object and return to the aircraft before it can be processed, they experience substantial time delay in obtaining velocity data. Some such systems (for example, those utilizing the Doppler effect) must bounce the signals off of objects located ahead of the aircraft and thereby may encounter the problem of getting no reflected signal back to the aircraft. This problem is particularly acute when attempting to bounce the signal off of flat horizontal surfaces, such as bodies of water. Also, these active systems inherently possess additional complexity and offer greater potential for failure, thus presenting increased risks as well as problems and costs associated with maintenance and system redundancy. Furthermore, some of these systems utilize moving detectors or a multiplicity of detectors for ground speed determination, adding further complexity which reduces system reliability.
Present wind shear determination systems rely on an inertial reference or ground generators coupled to an elaborate computational network. The time required to present the wind shear data to the flight crew by these systems is considerably more than is desirable for safe flying conditions.
SUMMARY OF THE INVENTION
This invention relates to an improved apparatus for accurately determining the ground velocity of an aircraft and avoids many of the disadvantages of the prior art.
The apparatus utilizes radiant emissions and reflections of the earth's surface, preferably in the optical and infrared regions. The apparatus first senses the radiant emissions and reflections of the earth's surface at two points in time; it then calculates the ground velocity of the aircraft from the relative shift of the sensed emissions and the reflections, the aircraft altitude, and the time delay between the sensing of the successive emissions; and finally it generates a signal indicative of the calculated ground velocity.
The apparatus for determining the ground velocity of an aircraft includes: means for detecting from the aircraft a first substantially instantaneous radiant energy contour of a first area of the earth's surface; the same means, or separate means analogous to the means for detecting a first contour, for detecting a second substantially instantaneous radiant energy contour, delayed in time with respect to the first contour, of a second area of the earth's surface, which second area overlaps in part with the first area; means for comparing the first contour with the second contour to determine the relative shift in position between the two contours; means for correcting the contour position shift by the aircraft altitude and for dividing the contour position shift by the time delay to obtain the ground velocity of the aircraft. Means for indicating the measured velocity is optional.
The apparatus provides a fast, reliable, simple and accurate, yet passive, means for determining the ground speed of an airplane. This system has no radiating parts and preferably no moving parts. Instead, the apparatus of this invention passively depends upon radiant energy, thereby eliminating the need for transmission equipment and the time delay, bulk, weight, and complexity that such equipment inherently adds to a system. As such, a system based on this invention is simpler, more reliable and hence safer than systems utilizing radiating and moving parts. Also, the method of determining the ground velocity utilized by this apparatus is simple, which further simplifies the apparatus necessary to perform it. This system determines the aircraft ground speed directly, independent of factors such as ground coefficient or airspeed, and thus its measurements are more accurate.
This measurement of the ground speed of an aircraft is especially useful during approach and landing when the aircraft is close to the ground. The system provides the data necessary for wind shear computation and real-time velocity and acceleration computations to be utilized by monitoring process controls, alarm systems, and anti-skid brake controls, among others, thus increasing the effectiveness of these systems and improving overall aircraft safety.
These and other advantages of the invention will become apparent during the following description of the presently preferred embodiment of the invention taken in conjunction with the drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a general representation of the operation of the preferred embodiment of the invention, as utilized by an aircraft;
FIG. 2 is a block diagram of the preferred embodiment of the invention;
FIGS. 3a and 3b show first and second contours generated by the preferred embodiment of the invention and their relationship;
FIG. 4 graphically represents the product-accumulation data which is the result of applying the preferred data processing method to the contours of FIGS. 3a and 3b;
FIG. 5 is a flowchart of the preferred method of determining the ground velocity of an aircraft.
FIG. 5a is a flowchart of a method of controlling the exposure time of the present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Turning now to the drawings, FIG. 2 shows a block diagram of the preferred embodiment of the aircraft ground velocity determination apparatus of this invention, designated generally as 10. The system 10 is an optical system responsive to light (preferably of near infrared wavelengths) reflected from or emitted by the earth's surface, including objects located thereon (see FIG. 1). The ground velocity of the aircraft is computed by the system 10 by optically tracking the aircraft 19 position change Δd as measured by the radiant energy incident to the system.
The system 10 is generally comprised of a lens system 12, a CCD (charge coupled device) camera or sensor 11, a signal processing unit 13, a sensor timing control unit 14, and a ground speed display unit 15.
The function of the lens system 12 is to focus impinging light 16 on the CCD sensor 11. As FIG. 1 indicates, the lens system 12 and the CCD sensor 11 are preferably mounted to an aircraft 19 in such an orientation that the field of view of the sensor 11 is centered substantially directly below the aircraft 19; the lens system 12 focuses the light 16 on the sensor 11; and the light 16 comprises an optical image of the surface of the earth beneath the aircraft 19. The lens system 12 and sensor 11 are shown in FIG. 1 in exaggerated form; in actuality, they are minute compared to the size of the aircraft 19. Preferably, the lens system 12 and the sensor 11 are rigidly mounted to the aircraft 19 such that the sensor 11 maintains a constant orientation or perspective perpendicular to the direction of flight of the aircraft 19. Alternatively, the lens system 12 and the sensor 11 may be gimbal mounted to the aircraft 19 such that the sensor 11 maintains a constant orientation or perspective perpendicular to the earth's surface.
The lens system 12 includes at least one lens 17 which preferably has a focal length required for the particular application. For close work, on the order of 10 feet, a 28 mm lens is desirable; for wind shear sensing in the landing pattern, 50 to 55 mm lenses are preferred; and for high altitude work, a 1000 mm lens is preferable. The lens preferably has a fixed focus and may have a plurality of segments. The one used for demonstration was a plastic Fresnel lens made by Melles Griot, 1770 Kettering St., Irvine, Calif. 92714. The preferred lens 17 is preceded by a filter 28 that rejects wavelengths below approximately 0.7 microns. Thus, the filter 28 allows substantially only near infrared wavelengths to reach the lens 17 while effectively rejecting blue wavelengths. This filtering helps to eliminate from the image seen by lens 17 scatter which is caused by fog, haze, rain, etc., and to which the shorter wavelengths, particularily blues, are susceptible. Hence the lens 17 sees a sharp image, virtually independent of atmospheric conditions.
The CCD sensor 11 is a linear image sensor and essentially functions as a camera. It detects or senses light 16 of the optical image which is focused on it by the lens system 12 and forms a record of the impinging image by essentially taking a "snapshot" thereof. The preferred CCD sensor 11 is the RL1024C/17 made by Reticon of 345 Potrero Ave., Sunnyvale, Calif. 94086. This preferred sensor 11 has a linear array of 1024 silicon photodiode detector elements, or pixels 18, arranged in a row. These particular silicon photodetectors are responsive substantially to wavelengths below 1.2 microns. Every other pixel 18, i.e., every odd-numbered pixel 18 of the 1024 pixels 18, is connected to a first analog shift buffer register 23, and the remaining pixels 18, i.e., the even-numbered pixels 18 of the 1024 pixels 18, are connected to a second analog shift buffer register 24.
Each silicon photodiode detector element of the preferred RL1024C/17 is 17 units wide and one unit long. Thus the preferred linear array of 1024 photodiode detector elements is a total of 1024 units long by 17 units wide. The 17 wide unit is preferred because it increases the amount of photons incident to the radiant energy sensitive area of the photodiodes and reduces the transverse shift of the image sensed by the photodiode detector elements. This arrangement results in greater resolution and hence more accurate readings of the radiant energy input data. Through experimentation it was discovered that 17 units was the optimal pixel width. If the pixel width is too wide, the resolution of the incident radiant energy image becomes smothered. On the other hand, as the pixel width decreases the resolution also decreases. In short, any pixel width greater than one unit is preferable up to a certain point and the most preferable range of pixel widths is 2 to 17 units.
Also, the maximum wavelength of radiant energy to which the preferred silicon photodiodes are substantially responsive is 1.2 microns. However, photodetector elements which are responsive to wavelengths above 1.2 microns are presently under development by others and this invention is intended to include those devices. Indeed, the earth's surface emits and reflects a substantial amount of radiant energy above 1.2 microns which this invention can utilize.
The light 16 which impinges on the pixels 18 causes the generation of electrons at each pixel 18. The amount of charge (i.e., the number of electrons generated) at each pixel 18 is linearily proportional to the intensity of light 16 falling upon that pixel 18 and the "exposure" time (i.e., the duration of the period during which the pixels 18 are enabled, or allowed to accumulate charges). The charges accumulated in the series of pixels 18 during the exposure time form a "snapshot" of a contour of the intensity of the light 16 which falls upon the CCD sensor 11. The contour "snapshot" is essentially an identifying signature of the object or area which generated or reflected the light 16.
As the pixels 18 are arranged serially in a row, the light intensity contour formed is a linear contour (i.e., a profile of a cross-section of the optical image falling on the sensor 11). The preferred sensor 11 is positioned on the aircraft 19 with the row of pixels 18 parallel to the longitudinal axis of the aircraft so that the profile is formed along the same axis. This profile is used to measure forward ground speed of the aircraft. Alternatively, sensors having multiple side-by-side rows of pixels (i.e., two dimensional pixel arrays) may be used. With such an arrangement of sensors, for example, every row of pixels may be utilized to form a separate contour. Or the sensed image can be integrated transversely across the rows of pixels (i.e., along each column of pixels) to take advantage of more light reaching the sensor and to thus obtain a more intense image. It is also possible to use the two-dimensional pixel array to form a two-dimensional, planar contour which can generate an indication of both the forward ground speed and lateral ground speed (lateral drift) of the aircraft.
The registers 23,24 are used to store the charges accumulated by their associated pixels 18. Because half of the pixels 18 are connected to the first register 23 and the other half are connected to the second register 24, each of the registers 23,24 may be utilized to store a separate contour generated by its respective pixels 18. This is done by staggering, or delaying in time with respect to each other, the points in time at which the associated pixels 18 of register 23 and register 24 are enabled take a "snapshot". This mode of operation may be explained by reference to FIG. 1. At time t1, the pixels 18 associated with the first register 23 are allowed to form a first light intensity contour 25 (see FIG. 3a). After a time delay Δt at time t2, the pixels 18 associated with the second register 24 are allowed to form a second light intensity contour 26 (see FIG. 3b).
Control of the CCD sensor 11, including control of the timing of the pixels 18 and the transfer of the accumulated charges from the pixels 18 to their respective registers 23,24, is executed by a sensor timing control unit 14. The sensor timing control unit 14 coordinates all of the timing parameters of the CCD sensor 11 and sends all of the necessary control signals to the CCD sensor 11. The preferred sensor timing control unit 14 is also manufactured by Reticon. The standard Reticon unit is modified to enable all the odd pixels in unison and all the even pixels in unison. The timing control unit 14 in turn operates under the direction of the signal processing unit 13, which computes the operational parameters for the CCD sensor 11 and commands its action. Thus the timing control unit is essentially an interface between the signal processing unit 13 and the CCD sensor 11.
As shown in FIG. 1, at time t1 the sensor timing control unit 14 allows pixels 18 associated with the first register 23 to become exposed to impinging light 16. This causes the detection and formation of the first light intensity contour 25 (see FIG. 3a) representative of a first area, portion 20, of the earth's surface lying in the field of view of the sensor 11 beneath the aircraft 19. At time t2, delayed with respect to time t1 by an amount Δt, the sensor timing control unit 14 allows the pixels 18 associated with the second register 24 to become exposed to the impinging light 16, thus causing the detection and formation of the second light intensity contour 26 (see FIG. 3b). As the aircraft 19 will have traveled a distance Δd during the time Δt, the field of view of the sensor 11 will have also moved by the distance Δd so that the second contour 26 is representative of a second area, portion 21, of the earth's surface beneath the aircraft 19. The delay Δt between the formation of the first and second contours 25,26 is controlled by the timing control unit 14 to assure that there is an overlap 22 between the first and second areas 20,21 of the earth's surface, and consequently that there is an overlap between the first and second contours 25,26. The relationship between the first and second contours 25,26 is shown in FIG. 3. Preferably, Δt is set such that the image is displaced approximately 100 pixels between the first and second contours. The operation of the timing control unit 14 in controlling the CCD sensor 11 is shown in the Initialization stages of the flowchart of FIG. 5. The operation of the timing control unit 14 will be further described below.
Upon command from the timing control unit 14, initiated by the signal processing unit 13, the charges in the pixels 18 which represent the contours 25,26 are transferred to the buffer registers 23,24, respectively. Upon further command from the timing control unit 14, the contents of the buffer registers 23,24 are serially read out in two sets as voltages, amplified, and transferred to the signal processing unit 13.
In the signal processing unit 13, the signals representative of the contours 25,26 are operated on by a digital computer 31 to derive therefrom the aircraft ground speed. The computer 31 is preferably based on the Z80B microprocessor made by Zilog, 1355 Del. Ave., Campbell, Calif. The computer 31 (Z80B) processes the input data, sets the system timing and performs data handling functions, as shown in the program listing attached as Appendix A. The program is flowcharted in FIG. 5, and an explanation of its operation is given below.
FIG. 3 shows two sets of real-time data obtained during the testing of a prototype device on an aircraft. These are pixel-by-pixel contours as viewed by the CCD sensor 11. FIG. 3a represents the first contour sensed at time t1 and FIG. 3b represents the second contour sensed at time t2. As shown in FIG. 2, the radiant energy profiles for these two sets of data are sensed by the CCD sensor 11 and the analog voltages representative of each profile are converted to digital form by the A/D (analog to digital convertor) 29. These sets of digitized data are then stored in memory 30 for processing. (For flight test purposes only, these sets of data were also digitally recorded on a small floppy disc in order to reproduce the data shown in FIG. 3.) These sets of digital data are then processed in the computer 31 and the correlator 32 to derive the ground velocity. The flow chart, FIG. 5, describes the data processing and computations involved in this process.
In the broadest terms, the processing of the data to derive therefrom the aircraft 19 ground velocity involves comparing the first contour 25 with the second contour 26 to determine the relative position shift between the two contours 25,26, denoted as Δn in FIG. 3. This contour position shift Δn is then corrected for the aircraft altitude to derive the actual distance Δd (see FIG. 1) traversed by the airplane 19 during the time Δt between the forming of the two successive contours 25,26. The traveled distance Δd is divided by the time Δt to obtain the aircraft's ground velocity.
The method used to determine the shift Δn is a cross-correlation function. For further reference, see K. Castleman, Digital Image Processing (1979).
Cross-correlation:
Given two functions f(t) and g(t), their cross-correlation function is given by ##EQU1## In a sense, the cross-correlation function indicates the relative amount of agreement between two functions for various degrees of misalignment (shifting).
The function g(t+π) is the function f(t) shifted in time by π. For this preferred embodiment, the function f(t) represents the first contour as the intensity of incident radiant energy as a function of time and the function g(t+π) represents the second contour as the intensity of incident radiant energy as a function of time. Thus, the second contour [g(t+π)] is the first contour [f(t)] shifted in time by π[Δt]. By multiplying these two functions, f(t) and g(t+π), and integrating the product over time, the amount of agreement or similarity between the two contours is obtained.
As shown in the above equation, the rigorous solution of the cross-correlation function is a continuous integral of the products of the two functions f(t) and g(t+π). However, a practical digital implementation can be achieved by using the TDC 1009J, a 12 bit multiplier-accumulator made by TRW, P.0. Box 2472, La Jolla, Calif. 92038. First, the digital data stored in memory 30 for the first contour 25 is multiplied (in the TDC 1009J) by the digital data in memory 30 for the second contour 26. In this process, each pixel data point of the first contour 25 (see FIG. 3a) is multiplied by the corresponding pixel data point of the second contour 26 (see FIG. 3b). For example, the pixel data point 1 of the first contour 25 is multiplied by the pixel data point 1 of the second contour 26, the pixel data point 2 of the first contour 25 is multiplied by the pixel data point 2 of the second contour 26, etc. Each contour 25,26 consists of 512 pixel points, and this multiplication process is repeated for each of the 512 corresponding pixel data pairs.
The multiplication of each pixel data pair is done one at a time, beginning with the first pair. The product of the first pixel data pair multiplication is stored in the accumulator of the TDC 1009J. Then the next pair of corresponding pixel data points are multiplied and the product is added to the number stored in the accumulator. After all the products of the 512 pixel data pairs have been added and stored in the accumulator, the magnitude of the number in the accumulator is stored in memory 30. The accumulator is then reset to zero; the data in contour 26 is shifted in time by one pixel; and the multiplication-accumulation process is repeated.
The final number in the accumulator after all 512 pixel data pairs have been multiplied and accumulated can be referred to as the sum of the products of each pixel data pair multiplication. This sum of the products represents the digital integration of the cross-correlation function, which represents the amount of agreement for the data representation of each contour 25,26 (i.e., the degree of similarity between the first contour 25 and the second contour 26). If the two contours were identical, there would be 100% correlation between them. But since the second contour 26 will be shifted in time with respect to the first contour 25 when the integration process begins, the degree of correlation of the first integration will be low. However, as the second contour 26 is incrementally shifted (one pixel at a time) in time with respect to the first contour 25 and the correlation calculation is repeated, the degree of correlation should increase as the two contours become more similar to each other. The number of pixel shifts necessary to achieve 100% correlation between the two contours will yield the value of the contour position shift Δn.
FIG. 4 illustrates the results of repeatedly applying this digital integration of the cross-correlation function to successive orientations of contours 25,26 (FIGS. 3a, 3b). It is shown that the degree of correlation actually decreases for the first few pixel shifts. But as the second contour is shifted additional pixels, the degree of correlation increases as the similarity between the corresponding points of the two contours increases. In this particular case the degree of correlation rises to a maximum of 81% after 55 pixel shifts. After this peak, the degree of correlation expectedly decreases as the two contours begin to shift "out of sync" with each other.
Note that the features of the contours 25,26 in FIG. 3 are not identical. Therefore, it is not possible to obtain 100% correlation between these two contours. In fact, 100% correlation is only attainable in theory. Physical limitations of the components which comprise the invention will preclude the attainment of perfect correlation in practice. However, the point at which the maximum correlation occurs can be used to determine the contour position shift Δn. That is, the number of pixels shifted to attain the maximum degree of correlation between the first and second contours represents Δn.
It is a simple matter to examine the final sum of products values stored in memory 30 for the maximum value and to determine the number of pixel shifts necessary to obtain the maximum value (55 in FIG. 4). Obviously, the maximum degree of correlation will not occur at the same number of pixel shifts every time. For accuracy, however, the time delay and exposure controls should be regulated to keep the number of pixel shifts necessary to attain the maximum degree of correlation less than one-third of the total number of pixels, and preferably less than 100 pixel shifts. As shown in FIG. 5, the computer 31 (Z80B) handles the data manipulation except for the product-accumulate function of the TDC 1009J.
The contour position shift Δn is proportional to the distance Δd traveled by the aircraft 19 in the time interval Δt between the formation of the two contours 25,26. To obtain the traveled distance Δd, the contour postion shift Δn must be corrected for the altitude of the aircraft and for the ratio of the focal length of the lens system 12 to the size of the image formed by the CCD sensor 11. The aircraft altitude is determined by the aircraft's altimeter and is input therefrom to the computer 31. The focal length-to-image ratio is a constant, equal to the lens system focal length divided by the length of the row of the CCD sensor's photodetector elements. To make the necessary corrections, the computer 31 multiplies the contour position shift Δn by the altitude and divides by the focal length-to-image ratio, thus obtaining the traveled distance Δd.
The ground velocity of the aircraft is equal to Δd/Δt: the traveled distance divided by the time it took to travel that distance, which is the time delay between the formation of the successive contours 25,26. Since the computer 31 controls the operation of the timing control unit 14, it determines Δt. Therefore, Δt is known. Thus, as the final step in the determination of the aircraft ground velocity the computer 31 divides the traveled distance Δd by the time delay Δt.
The computed aircraft ground velocity is output by the computer 31 as a digital signal. As shown in FIG. 2, the digital signal may be input to a numerical display 36 of the ground speed display unit 15 and to other logic systems of the aircraft (not shown). The digital signal may also be input to a digital-to-analog converter 37 in the signal processing unit 13. The D/A converter 37 converts the ground velocity signal from digital to analog form and outputs it to a display 38 of the ground speed display unit 15 and to other logic systems of the aircraft (not shown). Display 38, for example, may be a dial guage which displays the ground velocity in analog form.
As previously explained, the timing control unit 14 controls the time delay Δt to assure that there is overlap between the first and second contours 25, 26. The timing control unit 14 also controls the "exposure" time of the pixels 18 of the CCD sensor 11 to assure that the contour is properly exposed to obtain the sharpest contour which is best suited for contour feature recognition. The timing control unit 14 tries to prevent overexposure and underexposure, both of which can mask features of the contour. The "exposure" time is the period of time during which the pixels 18 are enabled to collect charges in order to form a "snapshot" of a light intensity contour. The exposure control of the timing control unit 14 is responsive to the contour average light intensity, or average mass, calculated by the computer 31 in the Initialization stage of contour processing in FIG. 5 which is shown in greater detail in FIG. 5a.
Referring now to FIG. 5a, when the system 10 is first activated, or turned on, the exposure control of the timing control unit 14 initializes the CCD sensor 11 operation by setting an initial exposure time as a function of the altitude of the aircraft 19. Short exposure time is set for low altitudes and long exposure time is set for high altitudes. After the initial pair of first and second contours have been formed, their average masses are computed. The signal processing unit 13 then computes the average of these two averages, or loop average, and compares the loop average to an upper threshold. If the loop average exceeds the upper threshold, the timing control unit 14 is commanded to cause the exposure time to be shortened; if the upper threshold is not exceeded, the exposure time is caused to be lengthened. The signal processing unit 13 repeats this procedure for the first three pairs of contours. After the fourth loop average mass has been determined, the signal processing unit 13 computes the combined average of the last four loop average masses, and compares the combined average mass to an upper and a lower threshold. If the combined average mass falls between the thresholds, the exposure time is not changed. If the lower threshold is exceeded, the timing control unit 14 is commanded to lengthen the exposure time, and if the upper threshold is exceeded, the timing control unit 14 is commanded to shorten the exposure time. The signal processing unit 13 continues this mode of operation for subsequent pairs of contours, computing the combined averages from the preceeding four loop averages.
To assure that the exposure time is adjusted for crisp image resolution (i.e., short exposure times at lower altitudes) and to further assure that the time between successive contours Δt allows sufficient overlap between the successive contours (i.e., a shorter Δt at lower aircraft altitudes) for a reliable and accurate measurement of the contour position shift Δn, the signal processing unit 13 controls the time delay Δt as a function exposure time and aircraft altitude. In response, the timing control unit 14 generates an exposure, readout, reset, exposure, readout, reset, etc. sequence of timing signals, which provides for the repeated generation of light intensity contours and the constant recalculation of the aircraft ground velocity therefrom.
Of course, it should be understood that various changes and modifications to the preferred embodiment described above will be apparent to those skilled in the art. For example, components manufactured by other manufacturers may be utilized to put together the apparatus. The sensor need not be a CCD sensor but may be any suitable photodetector or radiation detector. The photodetector need not be comprised of silicon photodiodes but any type of radiant energy sensitive device. The software may be changed to achieve similar operation in a different manner. For example, the contour position shift Δn could be obtained by identifying and isolating a particular feature in both the first and second contours and measuring its relative shift between the contours. Also, the program software will vary with the particular hardware used to make up the system apparatus. Different applications of the system are also feasible. For example, the system may be utilized to determine the speed of a ship, a ground vehicle, or the relative speed of any two objects. These and other changes can be made without departing from the spirit and the scope of the invention, and without diminishing its attendant advantages. It is therefore intended that all such changes and modifications be covered by the following claims.